Mencari nilai Z Tabel (Z alfa perdua)

Summary

This video explains how to determine the critical Z-value (Z tabel) used in hypothesis testing, particularly in large sample sizes. The speaker demonstrates how to calculate the Z-value using a significance level (alpha), and how to use a Z-table to find the corresponding Z critical value. With a focus on two-tailed tests, the explanation covers how to interpret the Z-value, compare it with the test statistic, and decide whether to reject the null hypothesis. The tutorial is aimed at helping students grasp the concept of Z-tests and critical values in statistical analysis.

Takeaways

• 😀 Z-table and critical Z-values are essential for hypothesis testing in statistics.
• 😀 The Z-table value depends on the significance level (alpha), not the calculated Z-value.
• 😀 To find the Z-table value, divide alpha by 2 (for a two-tailed test) and find the corresponding area.
• 😀 For an alpha level of 5%, divide it by 2 to get 2.5% (0.025), which corresponds to the shaded area on the normal distribution curve.
• 😀 The area of interest in the Z-table corresponds to 50% minus the alpha area (e.g., 50% - 2.5% = 47.5%).
• 😀 The value 0.475 is looked up in the Z-table to find the corresponding Z-value of 1.96.
• 😀 The critical Z-value for a 5% significance level is 1.96 for a two-tailed test.
• 😀 If the calculated Z-value (Z-hitung) is greater than 1.96, you reject the null hypothesis.
• 😀 If the calculated Z-value is less than 1.96 but still within the critical region, you fail to reject the null hypothesis.
• 😀 For an alpha level of 1%, the process is the same: divide alpha by 2 and look up the corresponding value in the Z-table.

Q & A

What is the purpose of the Z-test in statistics?

The Z-test is used in statistics to determine whether there is a significant difference between the sample mean and the population mean. It is typically used when the sample size is large (greater than 20).

How does the Z-table relate to hypothesis testing?

The Z-table helps determine the critical Z-value, which is used to define the rejection region in hypothesis testing. By comparing the calculated Z-value (Z hitung) to the critical Z-value, we can decide whether to reject the null hypothesis.

Why is the Z-table value dependent on the level of significance?

The Z-table value depends on the level of significance (α) because the critical Z-value corresponds to the probability threshold, which is set by the chosen significance level. The Z-value is based on the cumulative probability from the normal distribution curve.

What does the α/2 represent in the Z-test?

The α/2 represents the probability area in each tail of the normal distribution when using a two-tailed Z-test. For example, if the significance level is 5%, α/2 would be 2.5%, representing the area in each tail.

How do you find the Z-critical value for a given α level?

To find the Z-critical value, you first divide the significance level α by 2 (for a two-tailed test). Then, find the corresponding cumulative probability value (e.g., 0.475 for α = 5%) in the Z-table, which gives the Z-critical value.

What is the significance of the value 1.96 in the Z-test?

The value 1.96 is the Z-critical value for a significance level of 5% in a two-tailed test. This means that if the calculated Z-value (Z hitung) is greater than 1.96 or less than -1.96, we reject the null hypothesis.

How do you interpret the area under the curve in the Z-distribution graph?

In the Z-distribution graph, the area under the curve represents the cumulative probability. For example, 50% of the area is to the left of the mean, and the area in each tail (for a two-tailed test) represents α/2, which is used to calculate the critical Z-value.

What happens if the calculated Z-value is greater than the critical Z-value?

If the calculated Z-value is greater than the critical Z-value, it means the test statistic falls in the rejection region, and we reject the null hypothesis (H0).

How would the process change if the significance level α was 1% instead of 5%?

If α was 1%, the process would be similar, but you would divide α by 2 to get 0.5% (α/2). You would then find the corresponding cumulative probability value (0.995) in the Z-table and use the Z-critical value associated with that probability.

What does the Z-table provide in relation to the standard normal distribution?

The Z-table provides the cumulative probability for different Z-scores in the standard normal distribution. This helps identify the area under the curve to the left of a given Z-score, which is essential for finding the critical Z-value in hypothesis testing.